Recalling that the self-exciting terms of the intensities \(\lambda _t\)  and \(\mu _t\) 
are defined by exponential decay kernels,
even though the processes \(M\)  and \(S\)  does not have the Markov property themselves,
we are able to show that \((M, S, \lambda , \mu )\)  is a Markov process
(Errais et al. [1]}).
To get the Markov property of \((M, S, \lambda , \mu )\) ,
we derive its Dynkin formula,
in the next Proposition,
taking into account that this formula is a direct consequence of the strong Markov property and, hence, it
builds a bridge
between differential equations and Markov processes,
(see for instance, Øksendal
[2]}, Section 7.4).
